Then $r(t) \leq R(t)$. Since $k > 0$ we have that $kr(t) \leq kR(t)$. So $kr(t) - R'(t) \leq kR(t) - R'(t)$. Multiplying both sides of this inequality by $-1$ yields and using the Fundamental theorem of Calculus to compute $R'(t)$ yields: